Without graphing, classify each system of equations as independent, dependent, or inconsistent. (please help me with these two!! I'm slightly confused)
{6y + 2x = 8
{12y + 4x = 4
and
{2 - 0.25x = 0.5y
{-1.5y = 1.5x - 3

Question

Without graphing, classify each system of equations as independent, dependent, or inconsistent. (please help me with these two!! I'm slightly confused)
{6y + 2x = 8
{12y + 4x = 4
and 
{2 - 0.25x = 0.5y
{-1.5y = 1.5x - 3

anonymous · Answer

The easiest way to solve this is by solving the system of equations either by substitution or elimination.

Let's take a look at the first one:
6y + 2x = 8
12y + 4x = 4

We can solve this by elimination if we multiply the top equation by -2 and then adding the two equations together. This will give us
0 + 0 = -12. This is not a true statement. The system if equations is inconsistent and therefore does not yield a solution. If there is no solution, then that means that these two lines are in fact parallel.

Can you try to solve the second one yourself using the same process?

pokiedokie · Answer

yes, but do I have to find a pattern for that one as well like with the first equation (being it multiplied by -2)?

anonymous · Answer

In a manner of speaking yes. When solving by elimination, you want to multiply by a factor so that if you add the two equations together, either the x's or the y's cancel. In the first set, multiplying by -2 and adding cancelled out both the x's AND the y's.

pokiedokie · Answer

im sorry for being a pain, but i would rearrange this equation so I can subtract/eliminate it, correct?

anonymous · Answer

Yes, it would certainly make it easier :)
0.5y = 2- 0.25x
-1.5y = 1.5x -3

It seems easier to cancel out the y. You don't have to multiply by a negative because they are already opposite signs. Try to do the rest and let me know if you're still having trouble :)

directrix · Answer

Study tool for later.  @pokiedokie

pokiedokie · Answer

thank you very much!! this is helpful

pokiedokie · Answer

@CShrix i got -1y = -1.25-1, did i mess up somewhere because this doesn't seem correct to me?

anonymous · Answer

You have to multiply the first equation by 3 first. Then when you add the two equations, there are no more y's in the equation. Then solve for x from there :)

pokiedokie · Answer

1.5y = 6 - 0.75x
-1.5y - 3 - 1.5x
________________
y = 3 - (-0.75)  ??

anonymous · Answer

1.5y-1.5y = 0.
So you have
0 = 3 + 0.75x

pokiedokie · Answer

whoops, sorry, so this would be inconsistent

pokiedokie · Answer

thank you so much!!